A Dynamic Virtual Channel (DVC) is just a pipe for sending data between the RDP Client and the server. The answer to both questions is Yes, but it is probably more work than you are expecting.
Regarding Question #1: The DVC is a "dumb" pipe between the client and the server. Where each is located is irrelevant. Using it to connect to a "Cloud" system is not a problem as long as you can access the server using RDP. To access the Web Service you will need to create at least 3 modules:
The application running on the client PC that wants to access the web service.
The DVC Plugin that will be loaded by the RDP Client
The proxy exe running in the users session on the terminal server that will actually make the call to the Web Service.
App on Desktop --> Calls to endpoint exposed by DVC pluging --> DVC Plugin Sends request to Terminal Server --> Executable on Server Calls Web Service --> Result is returned in reverse.
Regarding Question #2: Yes you can, but you have to write the plugin to do it and the process on the server to initiate it.